Context. The structure in density and temperature of protoplanetary disks surrounding low-mass stars is not well known yet. The protoplanetary disks’ midplane are expected to be very cold and thus depleted in molecules in gas phase, especially CO. Recent observations of molecules at very low apparent temperatures (~6 K) challenge this current picture of the protoplanetary disk structures.\udAims. We aim at constraining the physical conditions and, in particular, the gas-phase CO abundance in the midplane of protoplanetary disks.\udMethods. The light molecule H2D+ is a tracer of cold and CO-depleted environment. It is therefore a good candidate for exploring the disks midplanes. We performed a deep search for H2D+ in the two well-known disks surrounding TW Hya and DM Tau using the APEX and JCMT telescopes. The analysis of the observations was done with DISKFIT, a radiative transfer code dedicated to disks. In addition, we used a chemical model describing deuterium chemistry to infer the implications of our observations on the level of CO depletion and on the ionization rate in the disk midplane.\udResults. The ortho-H2D+ (11,0−11,1) line at 372 GHz was not detected. Although our limit is three times better than previous observations, comparison with the chemical modeling indicates that it is still insufficient for putting useful constraints on the CO abundance in the disk midplane.\udConclusions. Even with ALMA, the detection of H2D+ may not be straightforward, and H2D+ may not be sensitive enough to trace the protoplanetary disks midplane.
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